Thursday, December 19, 2013

This year has brought big changes for my classroom. It's the year I started getting my students to create their own geogebras, in an effort to deepen their learning and put them on the path of self-directed learning. I've had them use geogebra to explore various functions, and then I collaborated with our Physics teachers to have the kids create virtual projectiles. At first, I felt super excited about it all. And I still do, but now sometimes it feels like....so what? It feels like once they're done, that's it, the kids don't think about them or look at them or use them again. And if that's the case, was the work worth doing in the first place?

Moreover, am I just doing the digital version of those school projects my own kids did? The ones that took hours and tons of glue, clay, and papier mache to do, and which were displayed for a few days, then either immediately became landfill or collected dust in the house for a few years, and THEN became landfill. In either version, whatever learning happened seemed awfully short-lived.

But the last thing I want to happen is for all this year's fabulous student-created geogebras to start collecting digital dust. Not only because of the amount of work and real learning that went into creating them, but also because there's still so much learning that they can facilitate. I think the trick is to get them to USE their own work for deeper, self-directed, and self-powered learning. How to do that......

A few ideas I've come up with:

What's next for Physics:

Idea #1: Once they've created their projectile projects, it might be time to, in the words of our Physics Guy Andy Ross, "take the engine apart." For example, investigate what happens to the components as time varies by moving the t-slider in this: (here's the actual ggb):

Maybe the teacher could demo this first, then have the kids unpack their own projectiles in the same way. It would illuminate some very tricky concepts that I know they have trouble with:

that the horizontal velocity is constant (that pink text doesn't change as you move the t-slider)

that it's gravity (ie the -4.9t²) that causes the vertical position to first increase, then decrease

that gravity subtracts at first a little, then a lot as time goes on, from the vertical position

that at the apex, the vertical velocity is 0, even though that puppy's still moving

Idea #2: Have students use their own projectile ggbs to solve problems. As an experiment, I took a look at some of their assigned questions, and since I'm not familiar with Physics, I was looking at it kind of as a student. One of the questions was: "A metal ball is thrown horizontally at 44.4 m/s from a height of 2.2 m. What horizontal distance does it travel before hitting the ground?" In order to just picture the situation, I set it all up on my own ggb with those initial conditions:

α = 0°, y1 = 2.2 m, v = 44.4 m/s

...then moved the t slider, and watched for the moment when the projectile's y-coordinate was 0:
At this point, I could just read the answer to the question, that the horizontal distance at that time is 28.86 m. But of course that's not the way we want them to get the answer! However, doing this directed my attention on the time variable, and then I saw that the time was the key - that once I knew that, I could find the horizontal distance. Learning enhancement opportunity provided by this ggb: It helped me own the problem - I understood what I had to do. I had to find the time needed for it to hit the ground, then use that to find horizontal position.
Of course, using ggb on the test isn't possible, but maybe using it before would make these questions clearer and easier to solve. Visualization is so important, and key to owning a problem.

What's next for Math:

Don't ask them for answers, ask them for questions:

The awesome John Golden gave me this idea: Give them this, and instead of asking them to use it to find the solution set to an inequality, give them a solution set (ie x e -∞, 6] u [10, ∞) and ask them to find two different inequalities for which it is a solution.

Along the same lines: once they've made their own function explorer, have them set the sliders so that a & b aren't 1, and h & k aren't 0. Then type in a rule in the input bar that is equivalent to it but with different parameters.

Use the t slider to demonstrate domain. For example, for the square root function Why doesn't the point P show up until t reaches a certain value? Or why does P disappear when t reaches a certain value? What is that value? For the rational function, reinforce concepts like asymptotes - shouldn't the t-slider have a hole in it? (which is probably not possible yet in ggb. I had hoped that the t-slider would stop working when we hit an asymptote, but instead, it jumps over it. Wrong.)

Use their formulas for zeros to talk about equivalent expressions, and simplified expressions. They all may have had it right, but they didn't all look the same.

What's next for me:If I want them to use this tool to explore, I need to model it. So I'm going to start changing my "lessons" into something else altogether. They're going to look more like this from now on:

Instead of using slides in my voicethreads/videos, I'm going to use geogebra, and instead of supplying my students with accompanying notes to fill in, they'll get the geogebra in the video to play with. This way I can model using the tool and enable the kind of exploration I want them to do.

Monday, December 2, 2013

Here are the projects! I and my fellow LearnQuebec teachers, Kerry Cule and Andy Ross, have just received these joint physics-math projects.I am beside myself. Speechless, which doesn't happen a lot. Such variety - sports, nursery rhymes, video games, abstract art, pirate ships. And such creativity!Each caption is a link that takes you to the html5 version at geogebratube.org. They all work, so have fun!

An embarrassment of riches:Many questions and conversations arose in the course of this project. Some I plan to bring up to the whole class. And all came from the kids' own individual problems that they encountered along the way to trying to get their projectiles to fly. Some of these are ideas that I'm sure all physics teachers try to get across every time they do the unit, but I also think that some of these probably never would have even come up without this project as a backdrop. Riches beyond imagination!"My formulas are right, but my projectile won't fly!" Launch velocity has a threshold: You need a certain velocity to overcome gravity - if the greatest velocity your slider allowed was 12, your projectile won't go up practically at all, because gravity overcomes it almost immediately: eg at 2 secs y = 12 (2) sin 50 - 4.9 (2)² = -1.2 mSize of projectile: One student had a projectile whose diameter could be varied. Will that affect the path?Value of g: One student had a slider for g. When would we need to vary the value of g? And should it be 9.8 m/sec² over the moon?Dimensional analysis: What are the units of all the variables in the sliders? What must be the units along the axes?

Realistic values for variables - Why allow negative velocity, initial position, or time? Do they make any sense for your situation? Under what circumstances would those make sense?Frame of reference - Not every student used the first quadrant as the location of their situation. Is that ok?Angle - some allowed their angle to go up to 360°. Does that make any sense for this context? Under what circumstances would it make sense?Other stuff: One student's projectile was an arrow, and one was a rocket. Super bonus: How to get them to move realistically along their flight pats? eg it begins with the tip pointing up and other end down, then they slowly reverse. Two different points joined by a segment? And what would be the difference between the coordinates of those two points? One has an angle that's the other one delayed, by a phase shift perhaps?Math stuff: A couple of students defined the position of their projectile as the intersection between two lines - the vertical line x = horizontal position of the projectile at time t, and the horizontal line y = vertical position of the projectile at time t. Mathematically sound. Works. Never thought of that. Mind blown.

Next post will have student reflections about these projects - more riches. Any feedback would be hysterically appreciated, especially by these hard-working rocket scientists, literally!